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V6-10 Mathematics Grade 8 W1 - Lesson 4: Multiplying and Dividing Integers TEACHER KEY

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Page 1: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers

V6-10

Mathematics Grade8W1-Lesson4: MultiplyingandDividing

Integers

TEACHERKEY

Page 2: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers

ALL RIGHTS RESERVED

Copyright © 2010, by Alberta Distance Learning Centre, 4601-63 Avenue, Barrhead, Alberta, Canada, T7N 1P4. Additional copies may be obtained from Alberta Distance Learning Centre.

No part of this courseware may be reproduced or transmitted in any form, electronic or mechanical, including photocopying (unless otherwise indicated), recording, or any information storage and retrieval system, without the written permission of Alberta Distance Learning Centre.

Every effort has been made both to provide proper acknowledgement of the original source and to comply with copyright law. If cases are identified where this effort has been unsuccessful, please notify Alberta Distance Learning Centre so that appropriate corrective action can be taken.

IT IS STRICTLY PROHIBITED TO COPY ANY PART OF THESE MATERIALS UNDER THE TERMS OF A LICENCE FROM A COLLECTIVE OR A LICENSING BODY.

Mathematics Grade 8Version 6Preview/Review W1 - Lesson 4ISBN 1-891894-00-6

Publisher: Alberta Distance Learning CentreWritten by: Monica dHamraitReviewed by: Patty Rogerson

Project Coordinator: Donna SilgardPreview/Review Publishing Coordinating Team: Heather Martel and Nicole Mckeand

Alberta Distance Learning Centre has an Internet site that you may find useful. The address is as follows: http://www.adlc.ca

The use of the Internet is optional. Exploring the electronic information superhighway can be educational and entertaining. However, be aware that these computer networks are not censored. Students may unintentionally or purposely find articles on the Internet that may be offensive or inappropriate. As well, the sources of information are not always cited and the content may not be accurate. Therefore, students may wish to confirm facts with a second source.

MaterialsRequired

ProtractorRulerCalculator

ImportantConceptsofGrade8Mathematics

NoTextbookRequired

Thisisastand-alonecourse.

W1 - Lesson 1 ..................................................Perfect Squares and Square RootsW1 - Lesson 2 ...................................................... Working with Ratios and RatesW1 - Lesson 3 ............................................... Multiplying and Dividing FractionsW1 - Lesson 4 ................................................. Multiplying and Dividing IntegersW1 - Lesson 5 .................................................................... Working with PercentsW1 - ReviewW1 - Quiz

W2 - Lesson 1 ..... Modelling and Solving Linear Equations Using Algebra TilesW2 - Lesson 2 ................................................................Solving Linear EquationsW2 - Lesson 3 .....................................Graphing and Analyzing Linear RelationsW2 - Lesson 4 ........................................... Critiquing the Representation of DataW2 - Lesson 5 ................................................. Probability of Independent EventsW2 - ReviewW2 - Quiz

W3 - Lesson 1 ..................................................................... Pythagorean TheoremW3 - Lesson 2 .................................................................Calculating Surface AreaW3 - Lesson 3 ..........................................................................Calculating VolumeW3 - Lesson 4 ........................................................................Drawing 3-D ObjectsW3 - Lesson 5 ...................................................................Congruence of PolygonsW3 - ReviewW3 - Quiz

Page 3: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers

Preview/Review Conceptsfor

Grade Eight Mathematics

W1 – Lesson 4:

Multiplying and Dividing Integers

Teacher Key

Page 4: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers

OBJECTIVESBy the end of this lesson, you will be able to:

• Apply rules for multiplying and dividing integers

• Solve an expression involving integers and apply the order of operations

• Solve problems involving the multiplication and division of integers

GLOSSARY

BEDMAS – an acronym that is used to apply the order of operations.

Dividend – the number that is being divided by another number.

Divisor – the number by which a dividend is divided.

Factors – the numbers that are multiplied to give a product. A factor of a given number will divide into the given number with no remainder left over. For example, the 4 and 5 are factors of 20.

Product – the answer that results when numbers are multiplied.

Quotient – the answer that results when numbers are divided.

Page 5: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers

Developed by Alberta Distance Learning Centre ....................................................................................................... 1

Preview/Review Concepts W1 - Lesson 4 MathematicsGrade8

W1 – Lesson 4: Multiplying and Dividing Integers

Materials required:

• Paper, Pencil, and Calculator

Part 1: Multiplying Integers

Multiplying integers involves a similar process as multiplying whole numbers. The only difference is that you have to watch the signs of the factors to decide whether the answer will be positive or negative.

Apply the following sign rules when multiplying integers:

• If there is an even number of negative signs, then the answer will be positive • If there is an odd number of negative signs, then the answer will be negative

Example 1

( ) ( )− × − = +4 3 12

There is an even number of negative signs.

The product is positive.

Page 6: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers

Preview/Review Concepts W1 - Lesson 4MathematicsGrade8

....................................................................................................... Developed by Alberta Distance Learning Centre2

Example 2

( ) ( )+ × − = −8 6 48

Practice Questions

1. ( ) ( )9 12+ × − =

2. ( ) ( )− × − =6 5

3. ( ) ( )3 11− × + =

4. ( ) ( )+ × + =12 7

There are an odd number of negative signs.

The product is negative.

( ) ( )+ × − = −9 12 108

( ) ( )− × − = +6 5 30

( ) ( )− × + = −3 11 33

( ) ( )+ × + = +12 7 84

Page 7: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers

Developed by Alberta Distance Learning Centre ....................................................................................................... 3

Preview/Review Concepts W1 - Lesson 4 MathematicsGrade8

Part 2: Dividing Integers

Dividing integers involves a similar process as dividing whole numbers. The only difference is that you have to watch the signs of the numbers being divided to decide whether the answer will be positive or negative.

Apply the following sign rules when dividing integers:

• If there is an even number of negative signs, then the answer will be positive • If there is an odd number of negative signs, then the answer will be negative

Example 1

( ) ( )+ ÷ − = −16 8 2

Example 2

( ) ( )45 9 5− ÷ − = +

There are an odd number of negative signs.

The quotient is negative.

There are an even number of negative signs.

The quotient is positive.

Page 8: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers

Preview/Review Concepts W1 - Lesson 4MathematicsGrade8

....................................................................................................... Developed by Alberta Distance Learning Centre4

Practice Questions

1. ( ) ( )− ÷ + =64 8

2. ( ) ( )42 6− ÷ − =

3. ( ) ( )+ ÷ − =24 6

4. ( ) ( )− ÷ + =75 25

( ) ( )− ÷ + = −64 8 8

( ) ( )− ÷ − = +42 6 7

( ) ( )+ ÷ − = −24 6 4

( ) ( )− ÷ + = −75 25 3

Page 9: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers

Developed by Alberta Distance Learning Centre ....................................................................................................... 5

Preview/Review Concepts W1 - Lesson 4 MathematicsGrade8

Part 3: Applying Order of Operations

When calculating the answer to an expression with many mathematical operations you must follow the order of operations. Use the acronym BEDMAS to help you.

B - bracketsE - exponentsD - divisionM - multiplicationA - additionS - subtraction

Example 1

Evaluate the following expression ( )23 12 11− + ÷ .

Step 1: Complete the operations found in the brackets.

( )23 12 11

11 11

= − + ÷

= − ÷

Step 2: Complete the division.

11 111

= − ÷= −

Complete these operations,divisions and multiplicationin order from left to right.

Complete these operations, addition and subtractionin order from left to right.

Page 10: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers

Preview/Review Concepts W1 - Lesson 4MathematicsGrade8

....................................................................................................... Developed by Alberta Distance Learning Centre6

Example 2

Evaluate the following expression (-12) - (5-32) + 32.

Step 1: Complete the operations found in the brackets.

( ) ( )( ) ( )

2

2

12 5 32 3

12 27 3

= − − − +

= − − +

Step 2: Solve the exponents.

( ) ( )( ) ( )

212 27 3

12 27 9

= − − +

= − − +

Step 3: Complete the subtraction.

( ) ( )12 27 9

15 9

= − − +

= +

Step 4: Complete the addition.

15 924

= +=

Page 11: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers

Developed by Alberta Distance Learning Centre ....................................................................................................... 7

Preview/Review Concepts W1 - Lesson 4 MathematicsGrade8

Practice Questions

1. ( ) ( )32 5 4 3− + − −

2. ( )( ) ( )− − − ÷ −2

2 9 3 12

3. − + ×25 10 7 3

4. - - - ¸( )34 5 45 15 3

( ) ( )

( ) ( )( )

= − + − −

= − + −

= + −

= − −= −

3

3

2 5 4 3

2 5 7

8 5 7

8 3543

( )( ) ( )

( ) ( )( ) ( )

( )

= − − − ÷ −

= − ÷ −

= − ÷ −

= − ÷ −

=

2

2

2 9 3 12

2 12 12

2 144 12

288 12

24

= − + ×= − + ×= − += − +=

25 10 7 35 10 49 35 10 1475 147

142

( )

( )( )

3

3

34 5 45 15

34 5 3

34 5 27

39 13596

= − − − ÷

= − − −

= − − −

= − +=

Page 12: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers

Preview/Review Concepts W1 - Lesson 4MathematicsGrade8

....................................................................................................... Developed by Alberta Distance Learning Centre8

Lesson 4: Assignment

1. ( ) ( )+ × − =36 3

2. ( ) ( )− × − =52 4

3. ( ) ( )− × + =17 5

4. ( ) ( )+ × + =22 10

5. ( ) ( )− ÷ − =66 11

6. ( ) ( )+ ÷ − =84 4

7. ( ) ( )− ÷ + =72 9

( ) ( )36 3 108+ × − = −

( ) ( )− × − = +52 4 208

( ) ( )− × + = −17 5 85

( ) ( )+ × + = +22 10 220

( ) ( )− ÷ − = +66 11 6

( ) ( )+ ÷ − = −84 4 21

( ) ( )− ÷ + = −72 9 8

Page 13: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers

Developed by Alberta Distance Learning Centre ....................................................................................................... 9

Preview/Review Concepts W1 - Lesson 4 MathematicsGrade8

8. ( ) ( )+ ÷ + =65 13

Solve the following problems.

9. At 2:00 pm in the afternoon the temperature outside was +24°C . Each hour the temperature decreased by 4 degrees. At what time was the temperature outside 0°C?

10. A submarine dives a depth of 24 metres every time it makes a plunge. How far beneath the water will it be if it makes 7 plunges?

( ) ( )+ ÷ + = +65 13 5

Step 1: Determine how many hours it took the temperature to reach 0°C .Divide +24°C by 4.

It took 6 hours for the temperature to reach 0°C.

Step 2: Determine what time the temperature reached 0°C.Add 6 to 2:00 pm.

2 + 6 = 8

At 8:00 pm, the temperature reached 0°C.

( ) ( )24 4 6+ ÷ − = −

Multiply the depth of each plunge by the number of plunges the submarine makes.

The submarine will be at a depth of 168 metres.

24 7 168− × = −

Page 14: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers

Preview/Review Concepts W1 - Lesson 4MathematicsGrade8

....................................................................................................... Developed by Alberta Distance Learning Centre10

11. Jocelyn owes her sister $250.00. If she pays her sister $50.00 every month, how many months will it take her to pay her sister back?

12. Ethan has $560.00 in his bank account. In one month he made 5 withdrawals of $65.00 each. How much money does he have in his bank account now?

13. ( ) ( )− − × − =212 5 6

Divide $250.00 by $50.00.

It will take Jocelyn 5 months to pay her sister back.

250 50 5− ÷ = +

Step 1: Determine how much money Ethan withdrew from his bank account.Multiply the amount of money he withdrew by the number of times he with-drew it.

-65.00 × 5 = -325.00

Ethan withdrew $325.00 from his bank account.

Step 2: Calculate how much money Ethan has in his bank account.Subtract his withdrawals from the total amount of money he had.

560.00 - 325.00 = 235.00

Ethan has $235.00 left in his bank account.

( ) ( )( ) ( )( )

= − − × −

= − − × −

= − +

=

212 5 6

12 25 6

12 150

138

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Developed by Alberta Distance Learning Centre ....................................................................................................... 11

Preview/Review Concepts W1 - Lesson 4 MathematicsGrade8

14. ( ) ( ) ( )− − × − ÷8 11 27 3

15. ( ) ( )( )− − × − ÷16 7 4 2

16. ( ) ( )36 4 6 3− ÷ − − ×

( ) ( ) ( )( ) ( ) ( )( ) ( )

= − − − × − ÷

= − − − × −

= − −

= −

8 11 27 3

8 11 9

8 99

107

( ) ( )( )( )( )

16 7 4 2

16 28 2

12 26

= − − × − ÷

= − + ÷

= ÷= −

( ) ( )( ) ( )( ) ( )

= − ÷ − − ×

= − − − ×

= − − −

=

36 4 6 3

9 6 3

9 18

9

Page 16: W1 - Lesson 4: Multiplying and Dividing Integers · W1 – Lesson 4: Multiplying and Dividing Integers Materials required: • Paper, Pencil, and Calculator Part 1: Multiplying Integers